We report a bimodality in the azimuthal angle distribution of gas around galaxies as traced by Mg II absorption: halo gas prefers to exist near the projected galaxy major and minor axes. The bimodality is demonstrated by computing the mean azimuthal angle probability distribution function using 88 spectroscopically confirmed Mg II-absorption-selected galaxies [Wr (2796) ≥ 0.1 Å] and 35 spectroscopically confirmed non-absorbing galaxies [Wr (2796) < 0.1 Å] imaged with Hubble Space Telescope and Sloan Digital Sky Survey. The azimuthal angle distribution for non-absorbers is flat, indicating no azimuthal preference for gas characterized by Wr (2796) < 0.1 Å. We find that blue star-forming galaxies clearly drive the bimodality while red passive galaxies may exhibit an excess along their major axis. These results are consistent with galaxy evolution scenarios where star-forming galaxies accrete new gas, forming new stars and producing winds, while red galaxies exist passively due to reduced gas reservoirs. We further compute an azimuthal angle dependent Mg II absorption covering fraction, which is enhanced by as much as 20%-30% along the major and minor axes. The Wr (2796) distribution for gas along the major axis is likely skewed toward weaker Mg II absorption than for gas along the projected minor axis. These combined results are highly suggestive that the bimodality is driven by gas accreted along the galaxy major axis and outflowing along the galaxy minor axis. Adopting these assumptions, we find that the opening angle of outflows and inflows to be 100° and 40°, respectively. We find that the probability of detecting outflows is ~60%, implying that winds are more commonly observed.